Emiel Claasen (MPI, Potsdam)
Modular Graph Forms (MGFs) are a class of modular forms represented by lattice sums associated to directed simple graphs. They originated from the calculation of graviton amplitudes in type II string theory. MGFs have remarkable mathematical properties such as an intricate network of algebraic and differential relations or the appearance of (conjecturally single-valued) multiple zeta values in their Fourier expansion. In particular, they are conjectured to arise as expansion coefficients of certain generating series dubbed equivariant iterated Eisenstein integrals. In this first of two talks, I will introduce the MGFs, talk about their appearance in string theory, and set the stage for their systematic conversion into their iterated integral representations.
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